Bulbapedia is your answer. The mod uses it, so you know it's good. (I suppose Serebii is also useful, but I find the wiki format better than game guides for the purpose of RP reference.)
Battles: Do you remember in the games and anime, when you patiently send out your pokemon, your opponent does the same, and you take turns using one of four attacks?
Battles in this game will primarily be 4v4, unless part of a war, in which case they will be far more massive. Trainers are targets, and often the best way to win is to take out the guy commanding the pokemon – it's like how they used to shoot officers in wars. (Consequently, defend yourself, and have your pokemon do so as well.) Your pokemon can use any attack it naturally knows, plus one egg move and one TM/HM move which you list in your application. (You can apply for an exemption if your pokemon has a terrible natural moveset. If I agree that it has one, I'll let you use more.)
Winning? Losing? Yeah, type advantages help. Level helps too – this isn't a dice game, but your level 1 pokemon won't take down a level 40 unless it's a Rattata.
But what you should really go for are inventive, cool strategies. Stuff like “Aim for the horn” in the anime, or... pretty much anything in pokemon special, which has ideas like “use Pikachu and Poliwrath to create a thundercloud, then use Venusaur's vines to collect the lightning and electrocute your opponent directly.”
Player vs. Player: There are no effective laws. People are struggling to survive. Characters will have personal antagonisms, as well. What does this mean?
Players will probably fight each other. Occasionally, I am sure, the players themselves will agree on a winner. But I anticipate that not many people want their characters to lose.
Post in this thread if a PvP match is going on and you need a referee. Referees can be players, but should not be ones with a personal stake in the match - if either players objects to the selection, they'll have to get a new ref. I'll do as many as I can, myself, and this will be one of the general modly duties if this RP gets big or complex enough that it has to have a mod team and not just a mod. Referees should generally post after both players have given orders, stating how well each player's techniques worked and what the battle looks like now, and not just a “who won” at the end of the match.